Question: A new type of band has been developed by a dental laboratory for children who have to

wear braces. The new bands are designed to be more comfortable, look better, and provide

more rapid progress in realigning teeth. An experiment was conducted to compare the mean

wearing time necessary to correct a specific type of misalignment between the old braces and

the new bands. One hundred children were randomly assigned, 50 to each group. A summary

of the data is shown in the table.

Old Braces New Bands

x 410 days 380 days

s 44 days 59 days

How many patients would need to be sampled to estimate the difference in means to within

26 days with probability 99%?